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Algebraic groups

This is an introduction to linear algebraic groups, a subject on the interface of group theory, linear algebra and algebraic geometry.

Learning Outcomes:

We cover the basic theory of linear algebraic groups over algebraically closed fields, including Jordan form and the Lie-Kolchin theorem, homogeneous spaces and quotient constructions, Borel subgroups, maximal tori and root systems. The necessary background in algebraic geometry will be developed from scratch along the way.